Problem: Solve for $q$, $ \dfrac{q + 1}{3q} = \dfrac{3}{5q} - \dfrac{1}{q} $
Explanation: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $3q$ $5q$ and $q$ The common denominator is $15q$ To get $15q$ in the denominator of the first term, multiply it by $\frac{5}{5}$ $ \dfrac{q + 1}{3q} \times \dfrac{5}{5} = \dfrac{5q + 5}{15q} $ To get $15q$ in the denominator of the second term, multiply it by $\frac{3}{3}$ $ \dfrac{3}{5q} \times \dfrac{3}{3} = \dfrac{9}{15q} $ To get $15q$ in the denominator of the third term, multiply it by $\frac{15}{15}$ $ -\dfrac{1}{q} \times \dfrac{15}{15} = -\dfrac{15}{15q} $ This give us: $ \dfrac{5q + 5}{15q} = \dfrac{9}{15q} - \dfrac{15}{15q} $ If we multiply both sides of the equation by $15q$ , we get: $ 5q + 5 = 9 - 15$ $ 5q + 5 = -6$ $ 5q = -11 $ $ q = -\dfrac{11}{5}$